Connected Bone Parenting Issue with IK Constraint
Have you setup the IK constraint's Chain Length setting? Its default value of 0 means the whole chain of bones, right up to its root which is the head, will be affected by the constraint. You'd need to limit it to whatever length of bones really need the IK behavior, in this case 1.



If you want to make eye target controller, IMHO a Damped Track constraint would be more appropriate than IK, because it works on a single bone and very easy to setup correctly. 

Each eye's bone need not be connected to the head, BTW.